15.2 - Born Haber cycles
15.2.1: Define the term lattice enthalpy. The sign of ΔH lattice indicates whether the lattice is being formed or broken.
The enthalpy change when 1 mol of an ionic lattice is formed from its component ions at an infinite distance apart.
M+(g) + X-(g) -> MX(s)
The value of lattice enthalpy is understood to be negative for the formation of the lattice (an exothermic - bond forming process), and positive for the breaking up of the lattice (an endothermic - bond breaking process).
Hess' law can also be aplied to the formation of ionic lattices via a series of steps. In the case of ionic substances this is called a Born Haber cycle.
lattice enthalpy increases with higher ionic charge and with smaller ionic radius (due to increased force of attraction). The smaller the ion the greater its charge density and the force of electrostatic attraction that it can exert.
Lattice enthalpy may be seen defined in two different ways, depending on the reference literature. For the IB it is defined as the energy released when 1 mole of an ionic substance is formed from its constituent ions at infinite separation.
Na+ + Cl- 
NaCl(s)
ΔH = -ve
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Each ion exerts an electrostatic field that attracts the oppositely charged ions. The ions are all drawn together into a giant lattice in which every positive ion is surrounded by negative ions and vice-versa. The animation only shows the first few ions in the lattice, but the process continues until all of the ions formed in the reaction are arranged in rows and columns - a giant ionic lattice. The energy released on forming the lattice is more than enough to compensate for any energy needed to ionise the sodium (in this case). |
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Animation showing the formation of a lattice
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15.2.2: Compare the effect of both the relative sizes and the charges of the ions on the lattice enthalpies of different ionic compounds. The relative value of the theoretical lattice enthalpy increases with higher ionic charge and smaller ionic radius due to increased forces of attraction.
The bond between ions of opposite charge is strongest when the ions are small.
The lattice energies for the alkali metal halides is therefore largest for LiF and smallest for CsI, as shown in the table below.
Lattice Energies of Alkali Metals Halides (kJ/mol)
| F- | Cl- | Br- | I- | |||||
| Li+ | 1036 | 853 | 807 | 757 | ||||
| Na+ | 923 | 787 | 747 | 704 | ||||
| K+ | 821 | 715 | 682 | 649 | ||||
| Rb+ | 785 | 689 | 660 | 630 | ||||
| Cs+ | 740 | 659 | 631 | 604 |
The ionic bond should also become stronger as the charge on the ions becomes larger. The data in the table below show that the lattice energies for salts of the OH- and O2- ions increase rapidly as the charge on the ion becomes larger.
Lattice Energies of Salts of the OH- and O2- Ions (kJ/mol)
| OH- | O2- | |||
| Na+ | 900 | 2481 | ||
| Mg2+ | 3006 | 3791 | ||
| Al3+ | 5627 | 15916 |
15.2.3: Construct a Born-Haber cycle and use it to calculate an enthalpy change.
15.2.4: Analyse theoretical and experimental lattice enthalpy values. A significant difference between the two values indicates covalent character.
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